Action-based quantum Monte Carlo approach to fermion-boson lattice models

费米子自由度和玻色子自由度之间的相互作用在凝聚态物理的许多领域起着重要的作用。一个关键的例子是固体中电子与晶格振动（声子）的耦合，这是超导或佩尔斯不稳定性等现象的基础。在这个项目中，我们将应用精确的数值方法来提高我们对不同费米子-玻色子模型的理解。例如，我们将研究未屏蔽的电子-声子相互作用对超导性的作用，或者声子对比热和热传输的温度依赖性的影响。此外，我们将研究由佩尔斯不稳定性主导的一维链向二维链的交叉。最后，我们将研究最近提出的由自旋涨落介导的高温超导模型。玻色子激发的无限数量，费米子和玻色子动力学的不同时间尺度，甚至对现代数值方法也提出了挑战。我们将使用连续时间量子蒙特卡罗方法，它特别适合研究复杂的费米子-玻色子问题。玻色子的自由度可以积分出来，得到一个纯费米问题，可以非常有效地模拟，没有系统误差。我们的结果有望与低维材料相关，如聚合物、二硫化物或铜超导体。此外，该方法的发展有望使将来研究其他复杂的费米子-玻色子问题成为可能。

The interaction between fermionic and bosonic degrees of freedom plays animportant role in many areas of condensed matter physics. A key example isthe coupling of electrons to lattice vibrations (phonons) in a solid, whichunderlies phenomena such as superconductivity or the Peierls instability.In this project, we will apply exact numerical methods to improve ourunderstanding of different fermion-boson models. We will, for example,investigate the role of an unscreened electron-phonon interaction forsuperconductivity, or the effect of phonons on the temperature dependence ofthe specific heat and heat transport. Moreover, we will study the crossoverfrom one-dimensional chains, which are dominated by the Peierls instability,to two dimensions. Finally, we will investigate a recently proposed model forhigh-temperature superconductivity mediated by spin fluctuations.The unbound number of bosonic excitations, and the different time scales ofthe fermion and boson dynamics pose a challenge even for modern numericalmethods. We will use a continuous-time quantum Monte Carlo method that isparticularly suited to investigate complex fermion-boson problems. Thebosonic degrees of freedom can be integrated out to obtain a purely fermionicproblem that can be simulated very efficiently, and without systematicerrors.Our results are expected to be relevant for low-dimensional materials such aspolymers, dichalcogenides, or cuprate superconductors. Moreover, themethodological developments are expected to enable investigations of othercomplex fermion-boson problems in the future.